连接结构接触界面非线性力学建模研究

连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因。由于连接界面力学行为的复杂性,以及对连接界面进行直接试验观测的困难,连接界面的力学建模一直是非常具有挑战性的科学问题。本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood和Williamson, GW)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比。然后考虑连接界面典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证。结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面非线性特征,并与有限元结果吻合较好。      

Thermally induced wrinkling in orthotropic layered plates with irregular delaminations

Delaminated regions figure prominently among potential threats to the structural integrity of layered plate configurations. Under a certain thermal loading threshold, geometrically nonlinear local instabilities in the form of buckling or wrinkling across the delaminated region crop up, giving rise to markedly amplified distributions of contour peeling stresses. The present paper aims to shed light on and quantify the manifold aspects and implications of the delamination-thermal-wrinkling trio. The paper faces the challenges of handling the nature of the layered configuration, the inherent geometrical irregularity of delaminated regions, the discontinuous interfacial conditions, the 3D stress state along the delamination contour, and the nonlinear evolution of local instabilities across an orthotropic delamination. For that purpose, a specially tailored 2D multi layered plate model and a corresponding triangular finite element are derived. The original contribution of the proposed model is in its ability to capture the thermally-driven, nonlinear small scale phenomena related to geometrically nonlinear response of the layered structure, using a 2D multi-layered plate theory solved with efficient 2D multi-layered triangular finite elements, as opposed to computationally expensive 3D finite element analysis. This is accomplished via the integration and synergy of methodologies that include: multi-layered high order plate theory to account for the layered layout, geometrically nonlinear strain-displacement relations to account for geometrical nonlinearities, orthotropic and thermo-elastic constitutive laws to account for thermal loads, and interlayer interface modelling which, combined with a the shear-locking free triangular FE, allows accounting for arbitrarily shaped delaminations. The model is validated against a 1D closed form solution and a 3D continuum based finite element analysis and is then used for a numerical study. In the study, the onset and the evolution of local instabilities in an adhesively bonded orthotropic layer across an irregular delamination are looked into. Special attention is given to the significant influence of material orthotropy and the relative directionality of the delamination on the threshold thermal load, the nonlinear wrinkling patterns, and the peeling traction distribution.     

Local mesh adaptation technique for front tracking problems

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh–Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data. © 1998 John Wiley & Sons, Ltd.     

Approximation and Calibration of Nonlinear Structural Dynamics

In this paper, a methodology for the calibration of nonlinear structural dynamic models is presented. Calibration of nonlinear structural dynamics offers several additional challenges beyond that of linear dynamics. Even with advanced computational power, exact nonlinear finite element simulations often take several hours to complete on engineering workstations. Thus, the proposed model calibration method utilizes an approximate structural model. This approximate analysis is embedded in the outer loop, which utilizes an exact finite element analysis to verify the validity of the approximate model. If the approximate model is shown to be invalid at that point in parameter space, then the new exact analysis is used to develop an improved approximate model and the inner loop is executed again. Specifically, this paper will focus on the two key aspects of the inner loop, namely the development of an approximate model, and the parameter identification using the approximate model.     

Finite element formulation for dynamics of delaminated composite beams with piezoelectric actuators

As a part of an effort to develop a model-supported method for detection of delaminations in composite beams with the use of time responses to external excitations, a finite element formulation for dynamics of a composite beam with delamination and attached piezoelectric actuators is developed. In this formulation account is taken of transverse shear deformation and nonlinear through-thickness variation of the longitudinal displacement. Parameters that characterize the delamination are incorporated into the formulation that makes the finite element model convenient for use in conjunction with damage identification (not discussed in the present paper). Computational predictions of frequencies show good agreement with experimental results.     

Non-homogeneous displacement jumps in strong embedded discontinuities

In this paper, strong discontinuities are embedded in finite elements to describe fracture in quasi-brittle materials. A new numerical formulation is introduced in which the displacement jumps do not need to be homogeneous within each finite element. Both the crack path and the displacement jumps are continuous across element boundaries. This formulation is compared with the discrete approach, in which interface elements are inserted to model the discontinuities, as well as with other embedded discontinuity approaches and with the partition of unity method. Numerical results have been obtained with relatively coarse meshes, which compare well with experimental results and with the results obtained from analyzes with interface elements.     

Finite element,stream function-vorticity solution of secondary flow in the channels of a rod bundle

A finite element method has been applied to predict the overall features of the fully developed turbulent flow in the non-circular channels of a rod bundle. The finite element discretization is based on the conventional Galerkin method using an isoparametric quadrilateral element with mixed interpolation. The primary axial flow and turbulent kinetic energy distributions have been predicted for fully developed turbulent flow conditions right up to the wall. The secondary velocity is represented by the stream function-vorticity formulation and the no-slip boundary conditions are explicitly introduced in the nonlinear equations by a boundary vorticity formula. The Newton-Raphson method is applied to the stream function-vorticity equations and solved simultaneously by the frontal solution technique. A one-equation eddy viscosity model of turbulence and an algebraic stress transport model have been used to predict primary axial velocity, secondary velocities and turbulent kinetic energy. The predictions obtained for a central subchannel of an equilateral-triangular rod array with p/d= 1.3 are in reasonable agreement with experimental data.     

Numerical simulations of tire-soil interaction based on critical state soil mechanics

The tire-soil interaction is numerically simulated using a modified critical state soil model, in conjunction with a new nonlinear elastic law and hardening law, implemented on a general purpose finite element program MARC. A nonlinear friction law is employed for representing the shearing behavior on the tire-soil interface. Numerical results show deformation patterns and stress distributions in the soil, as well as the normal and shear stress distributions on the tire-soil interface. Results obtained from numerical simulations of the tractive performance of tires at different slips on sand are also presented and compared with available experimental data.     

A thermomechanically coupled viscoelastic cohesive zone model at large deformation

A new viscoelastic cohesive zone model is formulated for large deformation conditions and within a fully coupled thermomechanical framework. The model is suitable for the simulation of a wide range of problems especially for polymeric materials. It can capture viscoelastic crack propagation as well as energy dissipation due to this process. Starting from the principles of thermodynamics, a 3D finite element formulation is derived for a fully coupled simultaneous solution of the thermal field and the deformation field. The viscoelastic model is constructed by extending an elastic exponential traction separation law using a simple rheology. The viscous part of the tractions is postulated to have the same characteristic length as the elastic part and that they are related by a single material parameter. A Newtonian dashpot is used to describe the evolution of the viscous separation. Furthermore, thermal effects are accounted for using temperature expressions in both the traction laws and the viscosity of the dashpot, and using a heat conduction law across the interface. The model is implemented within an implicit finite element code and the internal variable is calculated using an internal iteration. Different numerical examples are used to verify the model and a comparison with experimental data shows a satisfactory agreement.     

Nonlinear buckling of a spherical shell embedded in an elastic medium with imperfect interface

This work analyzes nonlinear buckling of a single spherical shell imperfectly bonded to an infinite elastic matrix under a compressive remote load. The inclusion is modeled using a nonlinear shell formulation and the matrix is treated as a linear elastic body. Imperfect bonding conditions are realized through a linear spring interface model. A variational method is used to derive the governing differential equations, which are cast into a tractable set of nonlinear algebraic equations using the Galerkin method. An incremental iterative technique based on the modified Newton–Raphson method is employed to find the critical load of the system. The accuracy and convergence properties of the proposed method are validated through finite element analysis. The study is relevant to the analysis of compressive failure of syntactic foams used in marine and aerospace applications. Results are specialized to glass particle-vinyl ester matrix syntactic foams to test the hypothesis as to whether microballoons’ buckling is a dominant failure mechanism in such composites under compression. Parametric studies are conducted to understand the effect of interfacial properties and inclusion wall thickness on the overall mechanical behavior of the composite. Comparisons between analytical findings and experimental results on compressive response of syntactic foams and isolated microballoons indicate that inclusion buckling is unlikely a determinant of compressive failure in vinyl ester-glass systems. In particular, the matrix is found to exert a beneficial stabilizing effect on the inclusions, which fail under brittle fracture before the onset of buckling.     

Thermomechanics of solids with general imperfect coherent interfaces

The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials.     

Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties

Mechanical problems involving an interphase between two well-defined, and eventually different, materials are of interest. The aim of this paper is to present a simplified model that, for low frequency regime, is appropriate for this situation: an interface model with elastic and inertial properties. We present, together with the equations of motion, an identification procedure that is valid for any mass density profile along the thickness of the interphase. For evaluating the accuracy of the model, computations of the reflection coefficients in some relevant cases are shown. Besides, a finite element method is used as a benchmark for both the high and low frequency regimes. It is worth to be noted that the numerical test has been inspired by the problem of the interphase that is formed at the bone-implant boundary.     

压电复合材料粘接界面断裂有限元模拟

根据数字化FRMM(Fix-Ratio Mix-Mode)断裂试验,得到了压电复合材料试件的断裂韧性和位移及应变场。本文在试验的基础上,通过非线性有限元软件ABAQUS及用户子程序UMAT进行了模拟分析,采用基于损伤力学的粘聚区模型(CZM)对压电复合材料界面的起裂和脱胶扩展进行了分析,并与VCCT方法进行了比较。计算得到的荷载位移曲线更接近于试验结果,但在裂纹扩展路径上的吻合需要对粘聚区法则进一步修正。通过进一步对CZM参数进行分析,表明界面粘结强度和界面刚度对计算结果的影响很大。研究结果表明,粘聚区模型可以很好地表征压电复合材料弱粘接界面脱胶断裂问题。     

A multi-fiber approach for modeling corroded reinforced concrete structures

Taking into account the specific behavior of the steel/concrete interface is of primary importance to predict properly the structural response of RC structures. Several constitutive models have been proposed in the literature within the framework of nonlinear finite element method (2D and 3D). Such approaches usually lead to high computational costs due to the large number of degrees of freedom. In the present paper, a multifiber-based model including the steel/concrete interface behavior is proposed. Despite the fact that the kinematics of the multi-fiber approach is based on the theory of beams, this simplified strategy accounts for local phenomena such as the relative sliding between concrete and steel. Furthermore, this steel/concrete interface constitutive model can be extended to model the loss of bond properties due to corrosion. The numerical implementation aspects are described and local responses at the Gauss point level are exposed in the cases of monotonic loadings with and without corrosion. The efficiency and the reliability of the proposed approach are tested on structural case studies which highlight a good agreement between numerical and experimental results. This multifiber-based model provides a pertinent tool for the engineers concerns with the structural assessment of degraded reinforced concrete structures.     

一类非线性系统载荷识别的组合迭代法

针对一类非线性系统提出了一种新的载荷识别方法,组合迭代法.该方法通过有限元方法和主动控制方法组合迭代来实现一类非线性系统的载荷识别.首先将非线性系统的有限元模型模态缩减成简化模型,由简化模型组成主动控制的被控对象;然后在选定的控制律下,设计控制调节器,使该系统监测点的响应功率谱密度达到预定谱,从而得到系统激励,即被识别的载荷;最后由非线性有限元响应验证载荷的合理性.对圆锥壳-包带组合系统载荷识别的数值研究表明了组合迭代法的有效性.该方法为导弹、宇宙飞船、航天飞机、火箭等航天航空结构振动试验的载荷识别提供指导作用,将促进航天航空事业的发展.     

An extended finite element method for modeling near-interfacial crack propagation in a layered structure

The extended finite element method (XFEM) is applied for the simulation of near-interfacial crack propagation in a metal–ceramic layered structure. An experimental evidence indicates that, in a ceramic–metal–ceramic sandwich structure, a near-interfacial crack in the ceramic layer can be drawn to or deflect away from the metal layer depending on the difference in elastic properties across the interface. To model near-interfacial fracture, only the Heaviside functions are used for the XFEM, and the vector level set method is employed for efficient evaluation of the enrichment functions. The crack propagation paths predicted by the XFEM simulation are found to be consistent with the experimental observation.     

Nonlinear behaviour of piezoceramics under weak electric fields. Part-II: Numerical results and validation with experiments

When excited near resonance in the presence of weak electric fields, piezoceramic materials exhibit typical nonlinearities similar to a Duffing oscillator such as jump phenomena and presence of superharmonics in the response spectra. In an accompanying paper, a generalized nonlinear 3D finite element formulation has been developed incorporating quadratic and cubic terms in the electric enthalpy density function and the virtual work done by damping forces. In this paper, the formulation has been validated by conducting experiments on test pieces of various geometries and of three different materials (in all, four case studies). Both proportional damping and nonlinear damping formulations have been used to predict the frequency response of these systems. Newmark-β method has been used to obtain the dynamic response of the systems using FE analysis. It is demonstrated that the nonlinear finite element model is able to predict the responses of the various test cases studied and the results match very well with those of experimental observations.     

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.     

A smeared / layered reinforced concrete model for finite element analysis

A new reinforced concrete model, in which the reinforcement steel is assumed as smeared / layered in concrete, is established and installed into a currently used finite element code for nonlinear analysis. It performs the nonlinear behaviors of both concrete and the reinforcement steel. The results of examples are in good agreement with the experimental data.     

Dynamic stability of spinning viscoelastic cylinders at finite deformation

The study of spinning axisymmetric cylinders undergoing finite deformation is a classic problem in several industrial settings – the tire industry in particular. We present a stability analysis of spinning elastic and viscoelastic cylinders using ARPACK to compute eigenvalues and eigenfunctions of finite element discretizations of the linearized evolution operator. We show that the eigenmodes correspond to N-peak standing or traveling waves for the linearized problem with an additional index describing the number of oscillations in the radial direction. We find a second hierarchy of bifurcations to standing waves where these eigenvalues cross zero, and confirm numerically the existence of finite-amplitude standing waves for the nonlinear problem on one of the new branches. In the viscoelastic case, this analysis permits us to study the validity of two popular models of finite viscoelasticity. We show that a commonly used finite deformation linear convolution model results in non-physical energy growth and finite-time blow-up when the system is perturbed in a linearly unstable direction and followed nonlinearly in time. On the other hand, Sidoroff-style viscoelastic models are seen to be linearly and nonlinearly stable, as is physically required.